An ultrasonic digital signal processing technique which can be used to size isolated inhomogeneities in an otherwise homogeneous medium is examined. The technique is known as Born inversion and is theoretically valid for application to weak scatterers. However, accurate radius predictions have also been obtained experimentally for strong scatterers (voids). The technique was examined using synthetically generated ultrasonic signals from weak and strong scatterers, as well as experimental data from voids in high strength metals, to ascertain the application limits of the algorithm and to investigate why the technique is insensitive to different classes of scatterer. It was found that the part of the frequency spectrum used in the inversion routine has a very similar profile for weak and strong scatterers. Accurate sizing using Born inversion is only obtained if the bandwidth of the interrogating probe is adequate. However, the probe bandwidth requirements depend on the size of the flaw being examined, which is not known a priori. A methodology is presented which determines whether the match of flaw size to probe bandwidth is suitable. This has proved critical in obtaining accurate size estimates from the inversion.

In circumstances where multi-layered structures play a critical role in the performance of manufactured components, a thorough and detailed inspection procedure is required. However the construction of such objects is such that it is not easy to provide an adequate non-destructive test to monitor the state of the structure. It is possible to employ x-ray techniques, but on these layered (or cylindrically symmetric) structures many exposures are required over a range of positions, which is both expensive and time consuming. It is therefore attractive to use an ultrasonic NDT system. A further important motivation for using ultrasound is its sensitivity to a large number of material parameters.

A formal yet widely applicable definition of inversion is difficult to find; this has led to Flax et al [l] to comment ‘Inverse scattering means many things to many people’. However, the inverse problem, viewed with particular reference to defect characterisation, can be regarded as gaining information on the features of an unknown or concealed body which can be made to cause a disturbance in an interrogating field. Thus imaging can be classed a non parametric inversion and indeed imaging and inversion processes have been shown to be mathematically equivalent under certain conditions [2]. Solutions to an inverse problem can be divided into two groups: direct and indirect. The direct method involves mathematical operations (usually transforms) for which the experimental data are the input and the interpretation of those data is the output. Indirect inversion, on the other hand, means finding the best fit between experimental data and a previously assumed theoretical model, and is usually an iterative process.

A pulse-echo (1D) Born inversion technique, which utilizes digital signal processing on ultrasonic back-scattered signals to size defects, is briefly outlined together with its application to the measurement of spheroidal defects in metals. The theoretical derivation of the algorithm is valid for application to weak scatterers; however, it is shown experimentally that this technique can give accurate radius predictions for strong scatterers such as voids. This apparent anomaly is examined using theoretically generated exact scattering data. A methodology for testing a specific transducer's suitability for sizing a specific defect is reported and demonstrated.